The following line passes through point $(1, -1)$ : $y = -\dfrac{7}{4} x + b$ What is the value of the $y$ -intercept $b$ ?
Solution: Substituting $(1, -1)$ into the equation gives: $-1 = -\dfrac{7}{4} \cdot 1 + b$ $-1 = -\dfrac{7}{4} + b$ $b = -1 + \dfrac{7}{4}$ $b = \dfrac{3}{4}$ Plugging in $\dfrac{3}{4}$ for $b$, we get $y = -\dfrac{7}{4} x + \dfrac{3}{4}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(1, -1)$